Question

$( \csc - \cot) {2} = 1 + cos \div 1 - cos \: prove \: that$
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Answer 1

Answer:

plz complete the question

Answer 2

Correct question :

$( \csc\:θ - \cot\:θ ) {2} = 1 - cos\:θ\div 1 + cos\:θ \: prove \: that$

Answer :

LHS :

→ $(\:cosec\:θ\:-\:cot\:θ\:)^2\:=\:(\:(\:1 \div sin\:θ\:)\:-\:(cos\:θ \div sin\:θ)\:)^2\:=(\:1\:-\:cos\:θ\:)^2 \div sin^2\:θ$

RHS :

→ $(\:1\:-\:cos\:θ\:)^2 \div 1\:-\:cos^2\:θ\:=\:(\:1\:cos\:θ\:)^2 \div (\:1\:-\:cos\:θ\:)\:(\:1\:+\:cos\:θ\:)\:=\:1\:-\:cos\:θ \div 1\:+\:cos\:θ$

☞ LHS = RHS

Hence proved.

♥ So, It's Done ♥ !!